International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 5 Issue 1, January-2016
Numerical study of simultaneous heat and mass transfer in absorption of vapor in laminar liquid film
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International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 5 Issue 1, January-2016
Sara Armou *1, Rachid Mir 1, Youness El hammami 1,
Sakina El hamdani 1, Kaoutar Zine-Dine 1
1Laboratory of Mechanics, Processes, Energy and Environment, National School of Applied Sciences
ENSA, B.P 1136, AGADIR, MOROCCO
*E-mail:
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International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 5 Issue 1, January-2016
Page | 1
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 5 Issue 1, January-2016
Page | 1
International Journal of Enhanced Research in Science, Technology & Engineering
ISSN: 2319-7463, Vol. 5 Issue 1, January-2016
ABSTRACT
A numerical investigation has been performed to study the combined heat and mass transfer in a falling liquid film absorption in aqueous lithium bromide solution flowing downward inside a vertical channel. The parabolic governing equations are solved for steady, two-dimensional laminar flow using the finite volume method. In the studied model, the coolant flows from bottom to top of the plate on which trickles film rich solution of lithium bromide and water vapor is absorbed by the film at the interface liquid-vapor. The heat release at the interface being mainly due to the water vapor phase change enthalpy. The numerical results indicate that the temperature distribution is the lowest at the wall and increases to the highest at the interface due to the heat absorption released at the interface and the concentration distribution is the highest at the wall and decreases to the lowest at the interface due to the water vapor absorbed at the interface. The effects of operating condition are presented and discussed and the result show that the absorption mass flux is higher for lower Reynolds number and increases with the increase of the inlet solution concentration, the system pressure and with the decrease of the inlet cooling water temperature.
Keywords: Absorption process, Falling film, Heat and mass transfer, Lithium bromide, Numerical simulation.
1. INTRODUCTION
The cold is used in various forms in large number industrial sectors and currently occurs with a compression system that uses electricity as important source of energy. These systems use refrigerants that have destructive effects, for these reasons it was necessary to use the absorption machines that represent an economical and efficient alternative for compression machines. Absorption refrigeration systems use fluids environmentally citing lithium bromide, ammonia, water or alcohols. The absorption machines are now the most widespread thermal refrigeration systems in several applications in the industry. These machines are running with an absorber, which is the most important element of the system which has a direct effect on efficiency, size, and manufacturing and operating costs of the system.
The development of absorption heat pump requires a better understanding of the combined heat and mass transfer process in absorption of LiBr/H2O. Many works concerning the study of falling film absorption have been made and from these works one can mention those of:
Shahram Karami et al. [1] numerically studied using the finite difference method the heat transfer and mass process in the steam absorption in a solution of LiBr, water-cooled on an inclined plate of the absorber. They found that the mass rate of absorption and the heat transfer and mass coefficients increase as the angle of the plate increases. Icksoo Kyung et al. [2] developed a model for the absorption of water vapor by the LiBr aqueous solution on a smooth horizontal tube using three different flow regimes. The calculation indicates the importance of droplet formation regime for predicting the absorber performance. K. J. Kim et al. [3] experiments were conducted on the water vapor absorption in an aqueous solution of lithium bromide (50% to 60% by mass) in the form of film flow on a vertical surface, while their results showed that the mass transfer coefficients are not different between 50% and 60% by weight LiBr solution. Shoushi Bo et al. [4] numerically investigated absorption process in the liquid film using CFD software package-Fluent, they have posed the convective boundary condition on the cooling water side and they have also studied the effect of variable physical properties on the process. The result is the overall rate of mass transfer of absorption is approximately 6.5% higher when properties are assumed constant. Raisul Islam et al. [5] experimentally studied two absorbers in similar conditions. The maximum increase of the steam vapor mass flow for the film-inverting design was about 100% compared to that of the tubular absorber. Marc Medrano et al. [6] have carried out an experimental study of the falling film absorption of aqueous solution of lithium bromide inside a vertical tube. They have found that in water-cooling thermal conditions the mass absorption fluxes are in the interval 0.001–0.0015 kg.m−2.s−1 while in air-cooling thermal conditions the interval of mass absorption values decreases to 0.00030–0.00075 kg.m−2.s−1. Liu Yang et al. [7] developed numerical model for the absorption of ammonia on a falling film for different ammonia-water mixtures containing nanoparticles and dispersants. The results show that when absorption pressure decreases or when initial concentration of mixture increases, the relative intensity of effect on absorption rate is weakened by the variation of thermal conductivity but enhanced by the variation of mass transfer coefficients and flow resistance, while the variation of mixture’s viscosity exhibits very low effect.
The present work focused on the simulation of the heat and mass transfer during absorption of vapor into liquid film of LiBr falling along a vertical channel. The conservation equations were used to determine velocity, temperature and concentration distribution within the film-thickness using the finite volume method. Effects of the four independent variables such as film Reynolds number, inlet solution concentration, inlet pressure and inlet cooling water temperature on absorption mass flux are presented in this paper.
2. MODEL DESCRIPTION
A. Physical model for absorber
The model of the problem studied is illustrated in Fig.1. At the top of the channel, a liquid solution is introduced; it flows down over vertical plate as a thin film of aqueous solution of lithium bromide, composed of absorbent (LiBr) and refrigerant (H2O).
The mass transfer process occurs at the interface of liquid film and vapor from the evaporator. The vapor is absorbed by the film and the heat produced due to this exothermic transformation is rejected by the external cooling water which flows countercurrent to the falling liquid film inside the channel.
The following assumptions have been taken into account in the formulation of the problem:
· The equilibrium condition exists at the interface.
· No shear forces are exerted on the liquid by the vapor.
· The flow of liquid film is considered laminar.
· The film thickness is considered constant.
· Heat transfer in the vapor phase is negligible compared to that in the liquid phase.
· The radiative transfer is negligible.
· Heat and mass transfer are two-dimensional.
Figure 1. Physical model
B. Mathematical modeling
Taking account of assumptions mentioned above, the governing equations described the flow and the heat and mass transfers corresponding to the continuity, momentum, energy and concentration in the liquid phase can be written as:
Continuity equation:
(1)
X-momentum equation:
(2)
Y-momentum equation:
(3)
Energy equation:
(4)
Concentration equation:
(5)
Where ρ, u, v, T, W, µ, cp, λ and D are respectively, density, axial velocity, transverse velocity, temperature, mass fraction LiBr in solution, dynamic viscosity, specific heat capacity, thermal conductivity and mass diffusivity; cp1 and cp1 are the specific heat capacity of lithium bromide and water respectively and g is the gravitational acceleration.
The film thickness is determined by Nusselt [8] theory and it’s described by the equation:
(6)
· Boundary conditions
The liquid phase equations (1)-(5) are subjected to the following boundary conditions:
Conditions to entry:and
At the inlet of the liquid film, the temperature and concentration of the film are uniform.
, , and (7)
Conditions at the wall: and
At the surface of wall, we have the no-slip and impermeable condition, so the gradient of concentration and the flow velocity are equal to zero.
, , and (8)
The wall temperature changes linearly and it’s determined by the equation as follows
Conditions at the interface: and
Interface equilibrium concentration can be obtained by a function of interface temperature and vapor pressure [9]:
(9)
Where
Equation (9) was solved iteratively using the Newton-Raphson root search method.
The continuity of energy at the vapor–liquid interface is expressed as follows:
(10)
Habs is the heat of absorption.
Where the interfacial absorption mass flux is calculated by the following equation:
(11)
Continuity of shear stress:
(12)
The velocity in x-direction:
(13)
Conditions at the outlet:and
, , and (14)
The local heat transfer coefficient from the interface to bulk solution along the film flow is expressed in terms of Nusselt number:
The local heat transfer coefficient from the bulk solution to tube wall surface along the film flow is expressed in terms of Nusselt number:
The local mass transfer coefficient from the interface to bulk solution along the film flow is expressed in terms of Sherwood number:
The bulk temperature and bulk mass fraction are defined as follows:
;
3. NUMERICAL METHOD AND GRID SIZE EFFECT
The system of equations (1)-(5) describing the heat and mass transfer with boundary conditions were discretized by finite volume method proposed by Patankar [10]. Integrating the governing equations, we obtained a system of algebraic equations written in the following compact form:
With:
We introduced an interpolation scheme for determining the values of the coefficients of the linear system; the coefficients are obtained by using a power law interpolation scheme. The sweeping method line by line, with the algorithm of Thomas was used for the iterative resolution of the systems of equations. The convergence criterion is that the maximal residual is less than 10-7.
A uniform grid was used in the domain with IN nodes in the transversal direction and JN nodes in the axial direction. To choose the best mesh that allows having the most accurate results, we studied respectively the influence of the grid size on the interface to bulk liquid heat transfer coefficient presented in Fig. 2 (a) and on the local Nusselt number shown in Fig. 2 (b). So we adopted for reasons of calculation accuracy amesh.
Figure 2. Influence of the grid size on. (a) the Interface to bulk liquid heat transfer coefficient and (b) the local Nusselt number
4. NUMERICAL RESULTS AND DISCUSSION
The main parameters of operating conditions used in the calculation in the present study are listed in Tab.1 and the physical properties of LiBr solution used are collected from [9]:
Table 1: Operating conditions
Parameters / RangesInlet solution temperature Tin / 45°C
Inlet solution concentration Win / 0.58-0.62
Reynolds number Rein / 10-100
Inlet pressure Pin / 0.5KPa-1KPa
Plate height H / 1m
Inlet cooling water temperature Tc,in / 32°C
Outlet cooling water temperature Tc,out / 36°C
C. Validation of numerical model
In order to verify the accuracy of the numerical procedure, a computer code were validated by comparing the results obtained on numerical study from the present model and those reported by Kawae et al. [11] and Yoon et al. [12]. A very satisfied agreement was observed between the different results. The small differences observed between the two results in terms of values of mass flux, temperature and concentration at the interface is less than 1%.
Figure 3. Comparison of interfacial temperature of present study with Kawae et al. [11]
Figure 4. Comparison of interfacial concentration of present study with Kawae et al. [11]
Figure 5. Comparison of mass flux of present study with Yoon et al. [12]
D. Temparature and concentration profiles
The profiles temperature Fig. 6 (a) is the lowest at the wall and increases to the highest at the interface liquid-vapor due the heat absorption liberated at the interface. The temperature gradient is high at the inlet and decreases toward the exit of the channel.
The concentration profiles for different location are shown in Fig. 6 (b), from the wall it can be seen that the concentration at the inlet remains constant; by approaching to the interface the vapor absorbed by liquid film reduces the concentration. The concentration gradient is high at the inlet and decreases toward the exit of the channel, due to end of the absorption.
Figure 6. Temperature profile (a) and concentration profile (b) across liquid film at Tin=45°C, Win=0.6, Rein=10 and Pin=1KPa
Fig. 7 (a) and (b) present the variation of temperature and concentration along the liquid film. The interface temperature is varying rapidly near the inlet region but gradually as the long of the plate increase due the heat absorption released at the interface, while the wall temperature varied linearly and the bulk temperature decreases slowly as y increases.
Similar distributions are spotted for the interface, bulk and wall concentration, the interface concentration decrease due the absorbed mass of vapor, the bulk concentration decreases at a slower rate because the mass boundary layer propagates slowly into the film due to low mass diffusivity. From y=0.2 all concentrations decrease linearly along the plate.